From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (majordomo@vger.kernel.org) by vger.kernel.org via listexpand id S262226AbVAJMl2 (ORCPT ); Mon, 10 Jan 2005 07:41:28 -0500 Received: (majordomo@vger.kernel.org) by vger.kernel.org id S262227AbVAJMl2 (ORCPT ); Mon, 10 Jan 2005 07:41:28 -0500 Received: from alog0069.analogic.com ([208.224.220.84]:34688 "EHLO chaos.analogic.com") by vger.kernel.org with ESMTP id S262226AbVAJMlP (ORCPT ); Mon, 10 Jan 2005 07:41:15 -0500 Date: Mon, 10 Jan 2005 07:41:02 -0500 (EST) From: linux-os Reply-To: linux-os@analogic.com To: "Patrick J. LoPresti" cc: Linux kernel Subject: Re: /dev/random vs. /dev/urandom In-Reply-To: Message-ID: References: <20050107190536.GA14205@mtholyoke.edu> <20050107213943.GA6052@pclin040.win.tue.nl> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: linux-kernel-owner@vger.kernel.org X-Mailing-List: linux-kernel@vger.kernel.org On Sat, 8 Jan 2005, Patrick J. LoPresti wrote: > linux-os writes: > >> In this case I AND with 1, which should produce as many '1's as >> '0's, ... and clearly does not. > > Actually, a fair coin flipped N times is unlikely to come up heads > exactly N/2 times, and the probability of this drops quickly as N > grows. > > What is true is that it will usually come up heads N/2 times, give or > take sqrt(N). Mathematicians call this the "Central Limit Theorem". > > For example, take N=32. The square root of 32 is a little less than > 6. So we expect to see between 16-6 (i.e., 10) and 16+6 (i.e., 22) > heads in a typical trial. (Of course, in one trial out of 4 billion > it will come up all heads. The Central Limit Theorem is about "usual" > outcomes, not every outcome.) > > So we expect between 10 and 22 odds/evens in your trial. > >> Trying /dev/random >> 0100000101010000010001000101000000000000000101000100010000000101 >> odds = 14 evens = 18 >> Trying /dev/urandom >> 0001010001000100000101000100010001000000000000000000010000000000 >> odds = 10 evens = 22 >> LINUX> ./xxx >> Trying /dev/random >> 0100000100010101000101010101010101000100010000010001010000000101 >> odds = 20 evens = 12 >> Trying /dev/urandom >> 0100000100000101010001000101010001010001000000010101010100010000 >> odds = 18 evens = 14 > > Well how about that. Try it with larger N, and you will find it gets > even harder to hit a case where the total is outside the sqrt(N) error > margin. And of course, as a percentage of N, sqrt(N) only shrinks as > N grows. > > If you doubt any of this, try it with a real coin. Or read a book on > probability. > > - Pat One is free to use any number of samples. The short number of samples was DELIBERATELY used to exacerbate the problem although a number or nay-sayers jumped on this in an attempt to prove that I don't know what I'm talking about. In the first place, the problem was to display the error of using an ANDing operation to truncate a random number. In the limit, one could AND with 0 and show that all randomness has been removed. However, those who know nothing about the theory would then probably jump upon this as a "special case" even though it usn't. Cheers, Dick Johnson Penguin : Linux version 2.6.10 on an i686 machine (5537.79 BogoMips). Notice : All mail here is now cached for review by Dictator Bush. 98.36% of all statistics are fiction.